All of the intervals in a scale have some sort of even frequency ratio. For example an octave is a 2:1 ratio. If we look at A4 (440 Hz), an octave up is just double that, so A5 is 880 Hz. An octave down is half, so A3 is 220 Hz.

The interval of a perfect fifth is a 3:2 ratio, which would be 440 x 1.5 = 660. A perfect fourth is 4:3, or 440 x 1 1/3 = 586 2/3. A major third is 5:4, or 440 x 1.25 = 550. Here's a nifty little chart I wrote up:

See how nice all that lines up? Now this is only in Just Intonation, which is not the system we use. The reason we don't use this system is because when you transpose it, some notes might be a little bit off from where they were in another key.

To make up for that, someone along the way came up with the system we use today, called Equal Temperament, specifically 12TET (12 tone ET), which divides the octave into 12 equal semitones, sacrificing the nice integer ratios that just intonation had for the notes in a single key. The advantage of this is that if you change keys you don't have to retune your instrument. However, since it doesn't use the precise ratios, certain intervals don't sound perfectly in tune (the major third is the biggest culprit of this), but at least they're equally out of tune in all keys. To the untrained ear, this difference is unnoticeable, but it would be noticeable in just intonation.

Anyway, if you're interested, the formula for the half-steps in 12TET is to multiply the given note by the twelfth root of 2 (or 2 to the 1/12th power) to get a semitone up, or change that 1 to however many semitones you want. For a perfect fifth, you would take your initial pitch (440 for example) and multiply it by 2 to the 7/12th power, which is roughly 1.498307, you get roughly 659.26 (although the decimal doesn't end there, it keeps going infinitely). See how that's not as nice a number as 660?

What I understood from the replies is that there is no logic behind this pattern. Probably, TTSTTTS was once formed by someone & named it as Major scale.

Regards,

Sarvagya Jain

It was actually invented by one Charles G. Major in the late 1700's. He invented a pattern of intervals that would be optimal for a perfect V-I cadence, and named the two central notes C and G, after his initials. He would then fill in the rest of the scale from A to G, reasoning that G was the letter for the perfect note, and was therefore unable to be surpassed. A prominent early adopter of this new scale was Wolfgang Amadeus Mozart, who wrote hundreds of pieces with it, even pushing new boundaries by starting the interval pattern on different notes of the Chromatic scale (much to the chagrin of James Chromatic, who was angered by the attitude people had taken in shoehorning his 12 tones into small boxes of pre-packaged sounds. His complaints were largely ignored by his peers.) For a while it was actually referred to as "the Mozart scale", but an early 19th century music history movement brought its creator back into the limelight and it became known as the Major scale.

Melodies were created. Those melodies used certain notes that people found appealing. Those melodies were handed down and passed around. Some were good and survived. Some were not so good and were either changed to sound better or were discarded

Most cultures share the pentatonic scale. It seems to be universally appealing to humans. Most likely this has to do with the chain of fifths and the harmonic series.

From there some cultures developed their musical palettes to include many more notes and some only a few extra notes. Our culture happened to develop melodic ideas that commonly used two extra notes on top of the pentatonic.

After some time and continuing cultural development of melodic ideas someone decided they would organize a this phenomenon into some kind of system. They looked at all those melodies and looked for commonalities. They arranged the notes into an order from lowest to highest and noted the similar distance between each of the notes. And we had scales.

This is all just hypothetical but I'm pretty sure it would have gone something along those lines.

The reason the semitones are where they are has to do with the pentatonic scale. Note that the semitones are spread as far apart as they can be from each other.

What I understood from the replies is that there is no logic behind this pattern.

Depends what you mean by 'logic'. If you mean 'an a-prior system of rules' then the answer is no. If you mean 'reasons why things ended up like that' then the answer is yes, except that the reasons are involved, complex and - to some extent - largely historical.

As far as being creative with interval patterns goes just feel free to do what you like. Music is an art, not a science, and the test of the art is what sounds good. If Messiaen can create chords by stacking one of each type of interval on top of one another (minor 2nd, major 2nd, minor 3rd, ..., major 7th, octave) I would say it's certainly something that's been explored by other composers with varying degrees of success.

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Quote:

Originally Posted by Hail

oh shut up with that /mu/ bullshit. fidget house shouldn't even be a genre, why in the world would it deserve its own subgenres you twat

It was actually invented by one Charles G. Major in the late 1700's. He invented a pattern of intervals that would be optimal for a perfect V-I cadence, and named the two central notes C and G, after his initials. He would then fill in the rest of the scale from A to G, reasoning that G was the letter for the perfect note, and was therefore unable to be surpassed. A prominent early adopter of this new scale was Wolfgang Amadeus Mozart, who wrote hundreds of pieces with it, even pushing new boundaries by starting the interval pattern on different notes of the Chromatic scale (much to the chagrin of James Chromatic, who was angered by the attitude people had taken in shoehorning his 12 tones into small boxes of pre-packaged sounds. His complaints were largely ignored by his peers.) For a while it was actually referred to as "the Mozart scale", but an early 19th century music history movement brought its creator back into the limelight and it became known as the Major scale.

Ah, but did you know Mr. Major was close friends with Mr. Alexsandr Edmund Minor, although later they fell out because Major came to believe Minor stole his best work?

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Quote:

Originally Posted by Hail

oh shut up with that /mu/ bullshit. fidget house shouldn't even be a genre, why in the world would it deserve its own subgenres you twat

What I understood from the replies is that there is no logic behind this pattern. Probably, TTSTTTS was once formed by someone & named it as Major scale.

Regards,

Sarvagya Jain

What I understood from this post is that you clearly didn't read all of the responses.

Sorry for the cynicism, but it's pretty true.

I like the way Sleepy Head put it. There is a lot of logic behind the pattern; in fact, way too much to explain if you want to go into the psychology about why our brain interprets certain sounds to be more pleasant than others or how certain sounds make us feel a certain way. In fact, a lot of that is still unknown. We just kind of accept it for what it is.

To sum up my post from earlier, a lot of it has to do with how the sound waves line up. For example, since an octave is exactly double the frequency, each wave of the lower note lines up with every second wave of the higher note in exactly the same place. That may be hard to understand without a visual, so here you go:

That is one cycle of the lower frequency (purple) and two cycles of the higher frequency (green). Notice where they both start their cycle. See how two cycles of the higher note line up with exactly one cycle of the lower note? That's what makes a harmonic octave have the kind of "ring" that it does. Here's another good visual:

Notice how the lowest C lines up with the one above it after one cycle (of the lower one. Now look at that second C to the G above it. Notice how it takes two cycles of the C to line up with the G? and three cycles of the G to line up with the C above it? and so on.

This is called the "harmonic series." Play the 12th fret harmonic on any string on a guitar. Hear how it's an octave up? If you measure from the nut to the 12th fret, you'll notice that it's the same distance as the 12th fret to the bridge. On a 24" scale guitar, that'll be 12 inches. It's an octave because you're dividing the string in half, effectively doubling the frequency. This is called the "first harmonic." The 7th fret harmonic is an octave and a fifth up from the open string and divides the string into three parts. The fifth fret is two octaves, divides the string into four parts.

You can actually see how the string vibrates in sections. If you play the fifth fret harmonic, you'll see that the string does not vibrate at the 12th fret. You can actually put your finger on the string there and the note will still ring out. That's actually what the second picture is showing. It's not the sound waves, it's actually showing the string vibrating in sections at all the harmonics. It's still a good way to visualize the sound wave though.

Asking for some "logic" (other than physics) behind the major scale pattern presumes a pre-existing musical frame of reference that would dictate the logic of scale patterns. It's actually the other way around - the major scale pattern dictates the logic for the rest of music. The major scale is a foundational concept in the written musical tradition.